I'm a bit cautious with stuff douwsed in chemicals, even if unscented there are still artificial detergents (not soap) on it. Lukewarm water or just a wet cloth will remove the dirt, some discoloration is just cosmetic and only matters if you are going to show the rabbit.
For discolaration I've read about rubbing in corn starch and combing it out. (Google "corn starch rabbit feet")